We collect some general results on graph limits associated to hereditary classes of graphs. As examples, we consider some classes defined by forbidden subgraphs and some classes of intersection graphs, including triangle-free graphs, chordal graphs, cographs, interval graphs, unit interval graphs, threshold graphs, and line graphs.

We study the class of 1-perfectly orientable (1-p.o.) graphs, that is, graphs having an orientation in which every out-neighborhood induces a tournament. 1-p.o. graphs form a common generalization of chordal graphs and circular arc graphs. Even though 1-p.o. graphs can be recognized in polynomial time, little is known about their structure. In this paper, we prove several structural results abo...

We consider uniform random cographs (either labeled or unlabeled) of large size. Our first main result is the convergence toward a Brownian limiting object in space graphons. then show that degree vertex cograph order n, and converges after normalization to Lebesgue measure on . finally analyze connectivity (i.e., minimal number vertices whose removal disconnects graph) connected cographs, this...

Let G be a simple graph and L = L(G) the Laplacian matrix of G. G is called L-integral if all its Laplacian eigenvalues are integer numbers. It is known that every cograph, a graph free of P4, is L-integral. The class of P4-sparse graphs and the class of P4-extendible graphs contain the cographs. It seems natural to investigate if the graphs in these classes are still L-integral. In this paper ...

A parallel algorithm to recognize cographs with a linear processor bound and a log’ II time bound is presented. This result extends the result of Adhar and Peng (1990). Moreover, we get a better time processor product than the algorithm of Lin and Olariu (199 I ). As a consequence distance hereditary graphs can be recognized by the same processor and time bound.

The notion of left convergent sequences of graphs introduced by Lovász et al. (in relation with homomorphism densities for fixed patterns and Szemerédi’s regularity lemma) got increasingly studied over the past 10 years. Recently, Nešetřil and Ossona de Mendez introduced a general framework for convergence of sequences of structures. In particular, the authors introduced the notion of QF -conve...

A graph is (m, k)-colourable if its vertices can be coloured with m colours such that the maximum degree of the subgraph induced on vertices receiving the same colour is at most k. The k-defective chromatic number χk(G) of a graph G is the least positive integer m for which G is (m, k)colourable. The Nordhaus-Gaddum problem is to find sharp bounds for χk(G)+χk(G) and χk(G).χk(G) over the set of...

In this commentary we make two rejoinders to Jung & Haier (J&H). First, we highlight the response selection component in tasks as a confounding variable that may explain the parieto-frontal involvement in studies of human intelligence. Second, we suggest that efficient response selection may be an integral part of the definition of

Tree representations of (sets of) symmetric binary relations, or equivalently edge-colored undirected graphs, are of central interest, e.g. in phylogenomics. In this context symbolic ultrametrics play a crucial role. Symbolic ultrametrics define an edge-colored complete graph that allows to represent the topology of this graph as a vertex-colored tree. Here, we are interested in the structure a...

Spiders are arthropods that can be distinguished from their closest relatives, the insects, by counting their legs. Spiders have 8, insects just 6. Spider graphs are a very restricted class of graphs that naturally appear in the context of cograph editing. The vertex set of a spider (or its complement) is naturally partitioned into a clique (the body), an independent set (the legs), and a rest ...